At 04:46 22.01.2004 +0200, Israel Nelken wrote:
>John Hershey's mail indicates the mathematical tools necessary to prove
>my claims. These can be found I think in the Papoulis book, for example.
Are you really sure that hearing can always be completely understood by
means of linear treatment of an arbitrarily chosen section of time? Do you
consider your retraction valid for any SPL, any variance, and any other
parameter?
Earlier you wrote:
"... consider the fact that a Poisson sequence of clicks has a flat
spectrum, like white gaussian noise, but sounds completely different."
I see a lot of discrepancy between our tools and physiology:
When we dealt with such clicks showing narrow peaks in excess of 140 dB SPL
with a 100 kHz microphone while simultaneously 14 dB less with a slower
one, we tried to improve the quality of recording by avoidance of clipping
in the sound card. This successful effort made the difference between the
original sound and the replay of its record tremendously worse. Dynamic
range of hearing amounts at least 120 dB, apparently outperforming any
linear audio equipment because perception of loudness is highly non-linear.
Perhaps, Robert Masta should not be too cautious with respect to true
amplitudes. I would rather ask for temporal and spectral limitations due
to the arbitrary choice of the temporal window being as a rule rather
different from physical and physiological restrictions.
If I am suggesting FCT and restriction to the real, i.e. elapsed, time
instead of FT and tacitly substituting the unknown future by mirrors of the
past, this might be seen as merely an uncommon odd point of view,
comparable to Feynman's notion of time running back and forth 'at a time'.
Maybe, I failed convincing you of correctness and usefulness of natural
spectrogram and joint autocorrelation. However, let's beware of blindly
keeping a book like that of Papoulis a bible of hearing.
Regards,
Eckard